VOLUME OF A FELLED TREE. 135 
sum of the volumes of all the sections will be the volume of the 
tree trunk. 
For example: A tree is felled at two feet above ground, and 
calipered at the stump and every four feet along the trunk down 
to three inches in diameter, and also at two feet above the last 
measurement. The remaining distance to the top of the tree is 
twelve feet.. (See Figure 37.) 
By reference to the table of areas of circles on page 136 the 
areas at each point calipered are found: 
Area at. diameter of oO incheés..........00c9+eeanmane serene -4418 
Atea at diameétet of 8 inchés: so0cc.cc0s. cuca a3 axa ewrxeses «3401 
Area-at-diameter of 7 incheSiey cceas dane viceanne nas eased 2073 
Area at diameter ‘of 6 inches: 2 cccs hes cand eee) oye en sae 1063 
Area at dianieter Of .$ AnCheSy:¢ ss.¢4ane at asosonsesdacenc slQ04 
Area at. diameter of 4 thcheSi..c..0006 cc saa ede acuainss owns 0873 
Area at diameter of-3 incheSc.assucestuses races seneaeadie 0401 
SUMO Psa reasey.a4c0.s sateen con ene cen acne ne ees 155273 
It will be noticed that these areas are taken at the middle of 
a four-foot section, so multiplying the sum by four, the volume 
of the trunk, from the ground to a height of 28 feet, is found 
to be 6.1092 cubic feet. Treating the top length of twelve feet 
as a cone, its volume is one-third times the basal area into the 
height,—.0341 X 12-+3=.1364 cubic feet,—which added to the vol- 
ume of the lower portion gives total volume of the tree 6.2456 
cubic feet. 
